Univariate spline quasi-interpolants and applications to numerical analysis

We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros

Continuous boundary elements for potential problems

Imperial Users onl

Investigation of the use of meshfree methods for haptic thermal management of design and simulation of MEMS

This thesis presents a novel approach of using haptic sensing technology combined with virtual environment (VE) for the thermal management of Micro-Electro-Mechanical-Systems (MEMS) design. The goal is to reduce the development cycle by avoiding the costly iterative prototyping procedure. In this regard, we use haptic feedback with virtua lprototyping along with an immersing environment. We also aim to improve the productivity and capability of the designer to better grasp the phenomena operating at the micro-scale level, as well as to augment computational steering through haptic channels. To validate the concept of haptic thermal management, we have implemented a demonstrator with a user friendly interface which allows to intuitively "feel" the temperature field through our concept of haptic texturing. The temperature field in a simple MEMS component is modeled using finite element methods (FEM) or finite difference method (FDM) and the user is able to feel thermal expansion using a combination of different haptic feedback. In haptic application, the force rendering loop needs to be updated at a frequency of 1Khz in order to maintain continuity in the user perception. When using FEM or FDM for our three-dimensional model, the computational cost increases rapidly as the mesh size is reduced to ensure accuracy. Hence, it constrains the complexity of the physical model to approximate temperature or stress field solution. It would also be difficult to generate or refine the mesh in real time for CAD process. In order to circumvent the limitations due to the use of conventional mesh-based techniques and to avoid the bothersome task of generating and refining the mesh, we investigate the potential of meshfree methods in the context of our haptic application. We review and compare the different meshfree formulations against FEM mesh based technique. We have implemented the different methods for benchmarking thermal conduction and elastic problems. The main work of this thesis is to determine the relevance of the meshfree option in terms of flexibility of design and computational charge for haptic physical model

Path Planning For Persistent Surveillance Applications Using Fixed-Wing Unmanned Aerial Vehicles

This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles (UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission, fixed wing vehicles have maneuver constraints that can limit their performance in this role. Current technology vehicles are capable of long duration flight with a minimal acoustic footprint while carrying an array of cameras and sensors. Both military tactical and civilian safety applications can benefit from this technology. We make three main contributions: C1 A sequential path planner that generates a C2 flight plan to persistently acquire a covering set of data over a user designated area of interest. The planner features the following innovations: • A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length • A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction • A smooth path generator that provides C2 routes that satisfy user specified curvature constraints C2 A set of algorithms to coordinate multiple UAVs, including mission commencement from arbitrary locations to the start of a coordinated mission and de-confliction of paths to avoid collisions with other vehicles and fixed obstacles iv C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing validated through flight test experiments on multiple platforms. A variety of tests and platforms are discussed. The algorithms presented are based on a technical approach with approximately equal emphasis on analysis, computation, dynamic simulation, and flight test experimentation. Our planner (C1) directly takes into account vehicle maneuverability and agility constraints that could otherwise render simple solutions infeasible. This is especially important when surveillance objectives elevate the importance of optimized paths. Researchers have devel oped a diverse range of solutions for persistent surveillance applications but few directly address dynamic maneuver constraints. The key feature of C1 is a two stage sequential solution that discretizes the problem so that graph search techniques can be combined with parametric polynomial curve generation. A method to abstract the kino-dynamics of the aerial platforms is then presented so that a graph search solution can be adapted for this application. An A* Traveling Salesman Problem (TSP) algorithm is developed to search the discretized space using the abstract distance metric to acquire more data or avoid obstacles. Results of the graph search are then transcribed into smooth paths based on vehicle maneuver constraints. A complete solution for a single vehicle periodic tour of the area is developed using the results of the graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm (C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and to ensure there are no collisions at any of the path intersections. We present a toolbox of spline-based algorithms (C3) to streamline the development of C2 continuous paths with numerical stability. These tools are applied to an aerial persistent surveillance application to illustrate their utility. Comparisons with other parametric poly nomial approaches are highlighted to underscore the benefits of the B-spline framework. Performance limits with respect to feasibility constraints are documented

Propagation and Control of Geometric Variation in Engineering Structural Design and Analysis

In this dissertation, we present a methodology for understanding the propagation and control of geometric variation in engineering design and analysis. This work is comprised of two major components: (i) novel discretizations and associated solution strategies for rapid numerical solution over geometric parametrizations of the linear and nonlinear thin-shell equations, and (ii) efficient surrogate modeling techniques and algorithms towards the control of geometric variation. While the methodologies presented are in the setting of structural mechanics, particularly Nitsche's method in the context of linearized membranes, Kirchhoff-Love plates, and Kirchhoff-Love shells, they are applicable to any system of parametric partial differential equations. We present a design space exploration framework that elucidates design parameter sensitivities used to inform initial and early-stage design and a novel tolerance allocation algorithm for the assessment and control of geometric variation on system performance. Both of these methodologies rely on surrogate modeling techniques where various designs throughout the design space considered are sampled and used in the construction of approximations to the system response. The design space exploration paradigm enables the visualization of a full system response through the surrogate model approximation. The tolerance allocation algorithm poses a set of optimization problems over this surrogate model restricted to nested hyperrectangles represents the effect of prescribing design tolerances, where the maximizer of this restricted function depicts the worst-case member, i.e. design. The loci of these tolerance hyperrectangles with maximizers attaining the performance constraint represents the boundary to the feasible region of allocatable tolerances. The boundary of the feasible set is elucidated as an immersed manifold of codimension one, over which optimization routines exist and are employed to efficiently determine an optimal feasible tolerance with respect to a user-specified measure. Examples of these methodologies for problems of various complexities are presented

Propagation and Control of Geometric Variation in Engineering Structural Design and Analysis

In this dissertation, we present a methodology for understanding the propagation and control of geometric variation in engineering design and analysis. This work is comprised of two major components: (i) novel discretizations and associated solution strategies for rapid numerical solution over geometric parametrizations of the linear and nonlinear thin-shell equations, and (ii) efficient surrogate modeling techniques and algorithms towards the control of geometric variation. While the methodologies presented are in the setting of structural mechanics, particularly Nitsche's method in the context of linearized membranes, Kirchhoff-Love plates, and Kirchhoff-Love shells, they are applicable to any system of parametric partial differential equations. We present a design space exploration framework that elucidates design parameter sensitivities used to inform initial and early-stage design and a novel tolerance allocation algorithm for the assessment and control of geometric variation on system performance. Both of these methodologies rely on surrogate modeling techniques where various designs throughout the design space considered are sampled and used in the construction of approximations to the system response. The design space exploration paradigm enables the visualization of a full system response through the surrogate model approximation. The tolerance allocation algorithm poses a set of optimization problems over this surrogate model restricted to nested hyperrectangles represents the effect of prescribing design tolerances, where the maximizer of this restricted function depicts the worst-case member, i.e. design. The loci of these tolerance hyperrectangles with maximizers attaining the performance constraint represents the boundary to the feasible region of allocatable tolerances. The boundary of the feasible set is elucidated as an immersed manifold of codimension one, over which optimization routines exist and are employed to efficiently determine an optimal feasible tolerance with respect to a user-specified measure. Examples of these methodologies for problems of various complexities are presented